The apparent coefficient of expansion of a liquid when heated in a copper vessel is C and when heated in a silver vessel is S. If A is the linear coefficient of expansion of copper, then show that the linear coefficient of expansion of silver is `(C+3A-S)/3`.

Explanation

The relation between the apparent coefficient of expansion `gamma_(alpha)` and real coefficient of expansion `gamma_(r)` is
`" "gamma_(r)=gamma_(alpha)+3alpha`
or, `" "gamma_(alpha)=gamma_(r)-3alpha, " ["alpha` is the linear oefficient of expansion of the material of the vessel]
In case of copper vessel, `C=gamma_(r)=3A`
In case of silver vessel, `S=gamma_(r)-3alpha^(.) " ["alpha^(.)` is the linear coefficient of expansion of silver (say)]
`therefore " "C+3A=S+3alpha^(.) " or, " alpha^(.)=(C+3A-S)/3`